Influence of the quality factor on the signal to noise ratio of magnetoelectric sensors based on the delta-E effect

Recently, there has been much interest in magnetoelectric magnetic field sensors utilizing the delta-E effect. Such sensors are fully integrable and combine the advantages of high sensitivity at low frequencies with broad bandwidth. Here, we report the influence of the quality factor Q on the signal-to-noise ratio of magnetoelectric magnetic field sensors utilizing the delta-E effect. The sensor consists of a silicon cantilever covered by a magnetostrictive and a piezoelectric thin film. The magnetization-dependent elasticity of the magnetostrictive film leads to detuning of the sensor's resonance, which is excited and read out via the piezoelectric layer. The signal-to-noise ratio is experimentally analyzed as a function of the quality factor, the excitation amplitude and the signal frequency. The results are compared with a signal and noise model to describe general tendencies. The model demonstrates that, in contrast to the conventional direct operation of magnetoelectric sensors, an improvement in the limit of detection proportional to Q^3/2 can be achieved if thermal-mechanical noise is dominant. The relationship still holds for frequencies far away from the resonance frequency. This reveals the potential for improving the limit of detection significantly by increasing the quality factor, if magnetic and electronic noise can be suppressed.